17 July 2008:

THE SOLUTION:

There are 40 humans and 30 rabbits. Let h be the number of humans, and let r be the number of rabbits.
Thus, we have two equations with two unknowns.

r + h = 70
4r + 2h = 200

We can multiply the first equation by 2 and subtract it from the second:

2r + 2h = 140
4r + 2h = 200

Thus, 2r = 60; r = 30; h = 40.

Are there other answers to this problem?



America and Russia are in an important race from Earth to Saturn. Both spaceships start at Moscow and end at Saturn. They start the race traveling at the same speed and neither of them speeds up or slows down. The result is not a tie. How is this possible?

maybe coz they start from MOSCOW from within there country....but seeing moscow ppl will assume that they both started frm MOSCOW, RUSSIA.

You never specified the time at which they started ....
Also Russia and america have a time difference of about 8-9 hours ....

18 July 2008:

THE SOLUTION:

The Americans and the Russians traveled different routes between the planets, and one route was shorter than the other. (You didn’t need much Maths Or General Knowledge for this one!) LOL!



NOT SO MUCH AS A TEST QUESTION BUT SOMETHING TO INTEREST YOU IN THE WORLD OF MATHEMATICS TODAY

The Norse god Odin tells you to pick any two-digit number. Multiply by 3, and use Odin’s mighty sword to sever the number so that you retain the last two digits of this result, and multiply by 3 again.

Repeat the process. For example, 13 becomes 39, then 117, which we cleave to 17. Thus, starting with 13, we produce 13 -> 39 -> 17 -> 51 -> 53 -> 59, . . .

How many steps does the starting number 13 take to return back to 13? Do such sequences always return to their starting numbers? If so, how many steps are usually needed?

19 July 2008:

THE SOLUTION:

Indeed, every starting two-digit number in the Odin sequence returns to itself eventually. Number 13
requires 20 steps to return; that is, the 21st number is the same as the first. All other two-digit starting numbers require 20 steps to return, except for multiples of 5, which behave differently and require fewer steps.



Monica is visiting her zookeeper friend Bill in the rain forests of Tanzania. Bill loves long-necked animals,
and his zoo is a strange one, for it consists of just two types of animal: giraffes and ostriches. Monica gazes across the wooded area. “How many animals do you have?”

Bill replies, “Among my animals, I have 22 heads and 80 legs in all. The number of ostriches is less than the number of giraffes. From this little information, can you tell me how many giraffes and ostriches I have?”

For the second problem, consider Bill’s other zoo in Kenya.

This zoo is filled only with long-necked birds. Monica is strolling with Bill through the Kenya zoo. “How many birds do you have altogether?” she asks.

“In my vast collection of birds, all but two of them are geese, all but two of them are swans, and all but two of them are ostriches. From my meager information, you should be able to find the answer.”

“Are you some kind of nut?”

“Not at all. Tell me the answer, and we’ll have a fine goose for dinner.”

20 July 2008:

THE SOLUTION:

Question 1: Bill has 18 giraffes and 4 ostriches. Each animal has 2 hind legs, so 22 heads means 44 hind legs
total. The remaining 36 legs must be the front legs of 18 giraffes. Therefore, 18 heads belong to the giraffes, and the remaining 4 heads belong to the ostriches.

Question 2: Altogether, Bill has 3 birds in his “vast” collection! Two of his birds are not geese, but 1 is. Two birds are not ostriches, but 1 is. Two birds are not swans, but 1 is. This adds up to 3 birds, 1 of each type.



Creatures from a nearby dimension penetrate our reality and want to fill a large swimming pool with their lime-scented nutritional fluid. From Hose A pours a green slime that would, by itself, take 30 minutes to fill
the pool. From Hose B surges a crimson slime that, by itself, would take 20 minutes to fill the pool. How long
would it take to fill the pool if both hoses poured at the same time?

The police will arrive at the scene in 15 minutes. If the creatures can fill the pool in under 15 minutes, they will deposit their spores in the liquid, multiply at fantastic rates, and take over Earth.

Will the creatures succeed in their plan for world conquest?

12 mins .... yes they will suceed.

BTW , nice imaginative way to present a simple problem.

21 July 2008:

THE SOLUTION:

It would take 12 minutes. The creatures will rule Earth. This is a classic problem that can be analyzed in a simple manner. If only Hose A is open, the portion of the pool filled by Hose A is T/30, where T is time. (Notice how after T = 30 minutes, the pool would be filled.) The portion of the pool filled by Hose B is T/20. When both hoses are open and the pool is completely filled, the equation to solve is
T/30 + T/20 = 1
Multiply by 60 to get
2T + 3T = 60 or T = 12
This means that the creatures will fill the pool in 12 minutes.

We can also think of many more complicated variations. For example, Hose A would fill the pool in 30 minutes by itself. Hose B would fill the pool in 20 minutes by itself. The creatures fill the pool in 3 minutes using Hose A, Hose B, and Hose C simultaneously. How long would it take to fill the pool using Hose C by itself?

Another question to ponder is what the approximate color of the fluid would be.



Bill is racing his poisonous Madagascar snail on a circular track that is 1 foot in circumference. The first time around, the snail travels at 30 feet per hour. How fast must the snail go the second time around to average 60 feet per hour for the two laps together?

22 July 2008:

THE SOLUTION:

The snail can’t go fast enough to average 60 feet per hour for both times around, no matter how hard it tries.
Here’s why.

60 feet/hour = 1 foot/minute.

To average 60 feet per hour, the snail would have to travel around the 1-foot track twice in 2 minutes. First, let us compute how much time the snail has taken to travel one lap. At 30 feet/hour (or 1⁄2 foot a minute), the snail has taken 2 minutes to complete the first lap, because the track is 1 foot long.

As we said, if we want the snail to travel at an average speed of 60 feet/hour (1 foot/minute), this requires that the two laps be completed in 2 minutes. If the snail needs more than 2 minutes to travel the two laps, it is traveling at a speed slower than 60 feet an hour. However, the snail has already used up 2 minutes to do one complete lap. This means it has used up all of its time. It can’t possibly complete two laps in 2 minutes. This means there is no way that it can achieve an average speed of 60 feet/hour.



Dr. Matrix is a godlike being with a brain so active that its glowing pulsations can be seen through his glassine skull. He is also able to create miniature universes. Dr. Matrix points to a shiny glass jar filled with
black holes and glowing stars, and nothing else. In other words, there are only two kinds of astronomical
objects to consider.

Dr. Matrix tells you that the percentage of black holes in his jar is more than 70 percent but less than 75 percent.

Can there be as few as seven astronomical objects in the jar? IE. If stars is denoted by x. Can x be = to 7?

23 July 2008:

THE SOLUTION:

Yes. Let us assume that there are x astronomical objects in the jar. Then, the number b of black holes is more than (70/100)x and less than (75/100)x. We can rewrite this as 70x/100 < b < 75x/100

We can rewrite this as the following by multiplying by 100:

70x < 100b < 75x
or
14x < 20b <15x

We want to find the smallest integer x such that 20b is in-between 14x or 15x, or, equivalently, the smallest possible number x such that the interval from 14x to 15x includes a multiple of 20. How might we do this?

The question was can x = 7. So let us assume (for now) that it is possible.

We then have from above : 98 < 20b < 105.

Now is there a multiple of 20 between 98 & 105. If there is then x = 7 is correct. A little thought reveals that 100 which lies betweem 98 & 105 is a multiple of 20.

Therefore x=7 & b=5 is correct.



In the Kama Sutra, an ancient Indian sex guide, we find a man who is tired of having sex, (can this ever be true) pausing and asking his lover: Oh beautiful maiden with beaming eyes, tell me, since you understand the method of inversion, what number multiplied by 3, then increased by three-quarters of the product,
then divided by 7, then diminished by one-third of the result, then multiplied by itself, then diminished by 52, whose square root is then extracted before 8 is added and then divided by 10, gives the final result of 2?

This is apparently a kind of mathematical foreplay. Can you solve the puzzle?

28 ..

mathematical foreplay .... lol

24 July 2008:

THE SOLUTION:

Number 28. When the man tells the woman how good she is with the method of inversion, he is referring to the idea of working a problem backward, so that when, for example, a divide operation is given, we actually multiply, and so forth.

To solve the Kama Sutra problem, we start with the answer 2 and work backward. When the problem says divide by 10, we multiply by 10. When we are told to add 8, we subtract 8. When told to find the square root, we take the square, and so forth.




A tiny disabled alien robot insect is attempting to climb over the edge of its spaceship, which is 40 feet tall. The creature starts at the base of the ship wall and takes a day to crawl 8 feet upward. The insect needs to recharge its fuel cells and so rests.

A month later, the insect awakens and realizes that it has slipped down 4 feet while sleeping. It begins its
upward journey, and 8 feet later it sleeps and falls down by 4 feet. If this happens every month, in about how many months will the insect reach the top of a 40-foot wall of its craft?

8months and 9 days....

25 July 2008:

THE SOLUTION:

In 9 months. The insect appears to be traveling upward by 4 feet each month. In 8 months, it will have traveled 32 feet from the base of the wall. However, on the ninth month, it will travel upward 8 more feet and reach the top of the wall.



You are partying in Goa, India—listening to Goa trance music—and suddenly see a group of Sikhs riding a total of thirteen tricycles and bicycles. You also see thirty-five wheels. How many tricycles do you see?

the answer for previous question is not 9 months .... after 8months and 8days .... that robot would have moved 32 feet. Now on the ninth day of that month he would move 8 feets up to make 40 feet.
So answer is 8days and 9months.


9 tricycles and 4 bicycles....